Analysis of sexual dimorphism of craniofacial traits using geometric morphometric techniques

Abstract

This work deals with the assessment of cranial sexual dimorphism in human skeletal samples applying geometric morphometric techniques. The purpose of this research is to apply such techniques to quantitatively describe in craniofacial traits the degree and pattern of shape and size sexual dimorphism. Likewise, we evaluate the precision and accuracy of semilandmark-based techniques for sex estimation. We employ a sample of 125 adult skulls of known sex from the Coimbra collection. A set of coordinate points was selected to describe glabella, mastoid, frontal and zygomatic processes. The results of intra-class correlation coefficient (ICC) show excellent intra- and inter-observer agreement (ICC > 0.96) in the location of the coordinates of points employed. The principal component analysis (PCA) performed on shape variables shows a large superposition of both sexes, suggesting a relatively low degree of dimorphism in shape. As a consequence, the average percentages of correct sex estimations based on these variables were of 60.12 and 68.90%, obtained by discriminant analysis with leave-one-out cross validation and k-means clustering respectively. Conversely, when centroid size is included in PCA, females and males exhibit large separation along the first component. The highest values of correct assignment (77.86 and 72.15%) were found using shape–size variables with discriminant and k-means clustering analysis, indicating that the traits analysed display marked sex differences related to the larger size and more robust features of males. Finally, the advantages of geometric morphometric techniques are discussed. Copyright © 2009 John Wiley & Sons, Ltd.

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Analysis of Sexual Dimorphism of
Craniofacial Traits Using Geometric
Morphometric Techniques
P. N. GONZALEZ,* V. BERNAL AND S. I. PEREZ
Divisio ´n Antropologı´a, Facultad de Ciencias Naturales y Museo, Universidad Nacional de La Plata. Paseo del
Bosque s/n, La Plata 1900, Argentina
ABSTRACTThis work deals with the assessment of cranial sexual dimorphism in human skeletal samples applying
geometric morphometric techniques. The purpose of this research is to apply such techniques to quantitat-
ively describe in craniofacial traits the degree and pattern of shape and size sexual dimorphism. Likewise, we
evaluate the precision and accuracy of semilandmark-based techniques for sex estimation. We employ a
sampleof 125adult skulls ofknownsex fromthe Coimbra collection. Aset ofcoordinate points wasselected to
describe glabella, mastoid, frontal and zygomatic processes. The results of intra-class correlation coefficient
(ICC) show excellent intra- and inter-observer agreement (ICC>0.96) in the location of the coordinates of
points employed. The principal component analysis (PCA) performed on shape variables shows a large
superposition of both sexes, suggesting a relatively low degree of dimorphism in shape. As a consequence,
the average percentages of correct sex estimations based on these variables were of 60.12 and 68.90%,
obtained by discriminant analysis with leave-one-out cross validation and k-means clustering respectively.
Conversely, when centroid size is included in PCA, females and males exhibit large separation along the first
component. The highest values of correct assignment (77.86 and 72.15%) were found using shape–size
variables with discriminant and k-means clustering analysis, indicating that the traits analysed display marked
sex differences related to the larger size and more robust features of males. Finally, the advantages of
geometric morphometric techniques are discussed. Copyright ? 2009 John Wiley & Sons, Ltd.
Key words: cranial sex; semilandmarks; discriminant analysis; k-means clustering
Introduction
To identify sex from skeletal samples correctly is very
important in bioarchaeological research. In this
context, the studies generally aim to establish the
sexual composition of large samples as well as to
compare the degree and pattern of sexual dimorphism
in different populations. Because sexual dimorphism is
not uniformly expressed in the skeleton, the accuracy
of estimations varies considerably between the
different osteological elements (Buikstra & Ubelaker,
1994; Meindl & Russell, 1998). Although the highly
dimorphic pelvic traits are considered to be the most
reliable sex indicator, the skull is frequently used in
archaeological contexts, due to its better preservation
(Novotny et al., 1993). In addition, numerous osteo-
logical collections formed in the last century are
composed exclusively by skulls and, as a consequence,
a great effort has been made to find criteria capable of
distinguishing male and female skulls either suggesting
new suites of traits or applying different morphometric
and statistic approaches to register and analyse the
cranial traits with acceptable levels of precision and
accuracy.
The protocol for sex estimation by visual assessment
of non-metric traits usually consists on seriating each
feature of the skull and then sorting them into
categories previously defined based on shape and size
differences (Buikstra & Ubelaker, 1994; Konigsberg &
Hens,1998;Grawetal.,1999;Grawetal.,2005;Rogers,
2005; Williams & Rogers, 2006). To obtain the final
estimation of sex, the traits used are ranked according
to their accuracy and precision (Rogers, 2005).
However, such approach has been largely criticized
for being highly subjective, and because quantitative
analysis of visual data is less developed than for metric
variables (Konigsberg & Hens, 1998; Williams &
Rogers, 2006). In addition, the seriation used to assign
International Journal of Osteoarchaeology
Int. J. Osteoarchaeol. (2009)
Published online in Wiley InterScience
(www.interscience.wiley.com) DOI: 10.1002/oa.1109
* Correspondenceto:FacultaddeCienciasNaturalesyMuseo,MuseodeLa
Plata, Paseo del Bosque s/n, La Plata (1900), Argentina.
e-mail: pgonzalez@museo.fcnym.unlp.edu.ar
Copyright # 2009 John Wiley & Sons, Ltd.
Received 4 February 2009
Revised 8 June 2009
Accepted 23 June 2009

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sex turns to be problematic when dealing with large
series, because it is doubtful that crania could be
seriated in any replicable manner, and each cranial
character must be examined independently (Konigs-
berg & Hens, 1998).
All that being said, it is often more desirable to
perform a metric analysis when working with
morphological data, since it has proven to be more
objective. Because measurements rely on standard
landmarks, results exhibit lower levels of intra- and
inter-observer error. Likewise there are more powerful
statistical methods for the analysis of continuous data.
Linear measurements are commonly evaluated by uni-
and multivariate statistical analyses, like discriminant
functions, which allow to separate sexes with a rather
high accuracy (Giles & Elliot, 1963; Franklin et al.,
2005). However, traditional linear measurements are
not able to capture the shape differences of some
complex and rounded structures, e.g. orbit shape, or
prominence of the glabella or chin. For that reason,
with a greater emphasis put on shape rather than size,
visual assessment methods provided the most valuable
tool to assess shape differences, at least until recently.
Because of these difficulties, researchers have
explored alternative methods of quantifying and
analysing morphological shape. A fundamental change
started in the 1980s, regarding the nature of the data
gathered and analysed (Rohlf & Marcus, 1993). Data
that captured the geometry of the morphological
structure employing 2D and 3D coordinates of
anatomicallandmarksandsemilandmarks(pointsalong
homologous surfaces, curves or outlines) were of
particular interest, and methods to analyse such data
were developed (Bookstein, 1991, 1997; Adams et al.,
2004). This approach, now called geometric morpho-
metrics, presents some advantages in relation to linear
measurements. Researchers can preserve geometric
information about the relative positions of coordinates
of points, visualise results of multivariate analyses as
configurations of landmarks back in the original space
of the organism, and assess variation in structures with
few or no landmarks (Adams et al., 2004). Thus,
geometric morphometrics would be more suitable to
describe subtle differences in sexually dimorphic
structures. Although some recent papers used land-
mark-based techniques to analyse the sexual dimorph-
ism of some cranial traits, the accuracy attained by
these techniques has not yet been evaluated (Rosas &
Bastir, 2002; Franklin et al., 2004; Katina et al., 2004;
Pretorius et al., 2006; Kimmerle et al., 2008).
The purpose of this research is to apply geometric
morphometric methods to quantitatively describe the
degreeandpatternofsexualdimorphismincraniofacial
traits. We evaluate the precision and accuracy of
semilandmark-based techniques
quantify shape and size differences between sexes in
a sample of adult skulls of known sex.
to describeand
Materials and methods
The sample consists of 125 adult skulls of known sex
(Table 1) randomly selected from the collection of
documented skeletons housed at the Museu Antropo-
logico de Coimbra (University of Coimbra, Coimbra,
Portugal). The Collection consists of 266 males and
239 females, with ages at the time of death that range
from 7 to 96 years old. The individuals used in this
study were born in Portugal between 1822 and 1921,
and died between 1904 and 1936 (Santos, 2000). The
majority of both males and females were from a lower
socio-economic class (Santos, 2000).
The specimens were photographed with an Olym-
pus SP-350 digital camera. The skulls were positioned
in the Frankfurt plane and the camera lens was oriented
paralleltothe sagittalplane usingaspiritlevel (Buikstra
& Ubelaker, 1994). The images from lateral view were
taken at a 300mm distance from the euryon point.
Coordinates for 12 landmarks (&) and 25 semiland-
marks (*) were obtained (Figure 1) to describe the
glabella, malar, mastoid process and frontal and
zygomatic processes.
These structures were chosen because: (a) they
exhibit high levels of preservation in archaeological
contexts (Paiva & Segre, 2003; Peterson & Dechow,
2003); (b) the influence of artificial cranial defor-
mation, a common cultural practice in several
populations, is smaller than in traits of cranial vault
and therefore generally negligible (Perez, 2006); (c)
previous studies suggest that these structures are
sexuallydimorphic (Buikstra & Ubelaker, 1994; Rogers,
2005; Williams & Rogers, 2006).
Digital images were processed with MakeFan6
(Sheets, 2003). MakeFan6 places alignment ‘fans’ at
Table 1. Age and sex composition of the Coimbra sample
Age (years)Female (n) Male (n)
15–19.9
20–24.9
25–29.9
30–34.9
35–39.9
40–44.9
45–49.9
>50
Total
3
7
3
7
10
8
10
4
4
4
50
16
9
14
10
8
8
75
Copyright # 2009 John Wiley & Sons, Ltd.
Int. J. Osteoarchaeol. (2009)
DOI: 10.1002/oa
P. N. Gonzalez, V. Bernal and S. I. Perez

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equal angular spacing along a curve to ensure a
consistent placement of semilandmark coordinates.
The landmark and semilandmark coordinates were
digitised by means of tpsDIG 1.40 software (Rohlf,
2007).
Within geometric morphometrics the shape is
defined as the information remaining after the effects
of position, orientation and scale have been held
constant (Rohlf & Slice, 1990). In this study, the
Generalised Procrustes analysis (Gower, 1975; Rohlf,
1990; Rohlf & Slice, 1990) was used to remove these
effects in landmark and semilandmark configurations,
and centroid size was employed as size measurement
(Bookstein, 1991). To convert the evenly distributed
points along contours into semilandmarks, they were
aligned by means of the perpendicular projection or
minimum Procrustes distance criteria (Sheets et al.,
2004). This operation extends the Generalised
Procrustes analysis (Gower, 1975; Rohlf & Slice,
1990) by sliding the semilandmarks until they match
as well as possible the positions of corresponding
points along an outline in a reference specimen,
minimising the Procrustes distance (Sheets et al., 2004).
Thisresultsinanalignmentofthesemilandmarksalong
the curve so that the semilandmarks on the target form
lie along the lines perpendicularly to a curve passing
through the corresponding semilandmarks on the
reference form (Sampson et al., 1996; Sheets et al.,
2004).
Shape differences between specimens were studied
using the aligned coordinates to perform a principal
component analysis (PCA) to describe major trends in
shape between males and females (Bookstein, 1991;
Rohlf, 1993). The principal components obtained from
these variables are known as relative warps (RW;
Bookstein, 1991; Rohlf, 1993). An important aspect of
thisanalysisisthatvariationalongtherelativewarpaxes
canbeexpressed asintuitivedeformationgriddiagrams
showingthedifferencefromthemeanformorreference.
To visualise sexual dimorphism, graphical representa-
tions of shape differences were generated as defor-
mation grids of female and male individuals relative to
the reference configuration (i.e. consensus configur-
ation).Inaddition,aPCAbasedonamatrixthatincludes
shape coordinates and an additional column with log
centroidsizewasmadetodescribethedifferencesinthe
shape–size space (Mitteroecker et al., 2004).
To estimate the precision of geometric morpho-
metric techniques, intra- and inter-observer error
associated with the placement of point coordinates
were evaluated independently. A general consensus on
methodologies suitable for assessing landmark and
semilandmark error has not been reached yet (see von
Cramon-Taubadel et al., 2007 for a discussion about
available methods). Whereas some methods evaluate
the individual landmark precision (Corner et al., 1992;
von Cramon-Taubadel et al., 2007), others emphasise
the analysis of the ‘overall effect of landmark error’
(O’Higgins & Jones, 1998; Lockwood et al., 2002;
Viðarsdo ´ttir et al., 2002;Gonzalez et al.,2007). The first
follows the same approach as traditional morpho-
metrics where the effect of discrepancy in data
recording is tested for each variable. However, in
geometricmorphometrics,itismoredifficulttotestthe
extent of observer-differences in data acquisition until
the configurations of landmarks are compared (von
Cramon-Taubadel et al., 2007). The second approach
does not provide information about the differential
precision of each coordinate, but it is a practical
approach to the overall effect of intra- and inter-
observer error on ‘individual specimen affinity’ (Lock-
wood et al., 2002). In this study, we follow the last
approach because observer error in semilandmarks
cannot be evaluated individually, and it allows us to
Figure 1. Allocated landmarks (&) semilandmarks (*) on cra-
niofacial structures. Landmarks: (1) frontex: most inferior
posterior midline point above glabella; (2) nasion; (3) frontoma-
lare anterior; (4) frontomalare temporale; (5) infraorbitale; (6)
zygomaxillare anterior; (7) the most superior point on the suture
between zygomatic process of the temporal bone and the
temporal process of the zygomatic bone; (8) the most inferior
pointonthesamesuturethatlandmarks7;(9)auriculare;(10)itis
defined as the point on the lateral aspect of the inferior border of
therootofthezygomaticprocess;(11)itisdefinedastheanterior
point on the root of mastoid process; (12) it is defined as the
posterior point on the root of mastoid process. Landmarks 2, 4
and 9 were digitised following Buikstra & Ubelaker (1994), land-
marks 3 and 6 following Howells (1973).
Copyright # 2009 John Wiley & Sons, Ltd.
Int. J. Osteoarchaeol. (2009)
DOI: 10.1002/oa
Sexual Dimorphism of Cranial Traits

Page 4

estimate whether observer error confounds the
discrimination of individuals in the sample.
In order to assess intra-observer error, P.N.G.
digitised the landmarks and semilandmarks on photo-
graphicimagesof30craniarandomlyselectedfromthe
skeletal collections hosed at the La Plata Museum. Two
sets of variables were obtained for each skull with a
week’s interval between the scoring sessions. Then, to
assess inter-observer error, the other authors (V.B. and
S.I.P) digitised the landmarks and semilandmarks on
the same sample. The sets of point coordinates
obtained each time were used to perform a relative
warps analysis, and the ordinations obtained were
compared to evaluate both intra- and inter-observer
error by comparing the score of each individual on the
first two relative warps using an intra-class correlation
coefficient (ICC; Shrout & Fleiss, 1979). Intra-class
correlation assesses rating reliability by comparing the
variability of different ratings by the same subject to
the total variation across all ratings and all subjects.
The ICC values range from 0 to 1, corresponding to
lowest and highest agreement, respectively. Signifi-
cance level was established as p<0.05 and indicates if
the agreement is greater than the one expected by
chance.
The accuracy of geometric morphometric tech-
niques was assessed by estimating the sex of individuals
using two statistical methods, discriminate analysis
with leave-one-out cross validation and k-means
clustering. Their performance was examined by
comparing the percentage of cases which estimated
sex correctly matched the actual sex of the skull (i.e.
the percentage of correct classification).
Discriminantanalysisisamethodusedtofindasetof
axes that grants the greatest ability possible to
discriminate between two or more groups (Manly,
1994). The main purpose of discriminant analysis is to
achieve a predictive classification of individuals. The
first step is to estimate the discriminant functions that
best discriminate between groups, computing the
classification scores for the individuals. The next step is
to classify the individuals according to the group for
which they have the highest classification score.
Finally, the accuracy of the classifications is evaluated
using a cross-validation analysis. In cross-validation,
each case is classified by the functions derived from all
cases other than that case. Therefore, the analysis is
performed several times, excluding one individual at a
time, as a way to establish whether or not it is well
classified. This gives an unbiased estimate of the
percentage of individuals that were wrongly classified.
The significance of discriminant functions can be
tested using Wilks’ lambda and F value.
Discriminantanalysismakessomeassumptionsabout
thevariablesemployed(i.e.lesspredictorvariablesthan
the sample size of the smallest group, lack of high
multicollinearity, normality and homogeneity of
covariance matrices) that must be tested before
performing the analysis. Because discriminant analysis
requires more individuals than variables per group, the
useofoutlinemethodsposesdifficultiesduebothtothe
largenumberofsemilandmarksperindividualneededto
describeoutlinesandtotherepresentationofsemiland-
mark points by two coordinates (x- and y-) when there
is only one degree of freedom per point (Sheets et al.,
2006).Therefore,principalcomponentsanalysisisused
to reduce the dimensionality of the data by analysing a
limited number of scores instead of the original data. In
addition, the use of principal components avoids
multicollinearity. In this study, the discriminant
analysis was based on the score of individuals along
thefirsttwoaxesofPCAobtainedforshapeandshape–
size (i.e. form) variables. We tested the normality
employing Kolmogorov–Smirnov test (Hair et al.,
1998). The results show that principal components
of shape (RW1: d¼0.04889; RW2: d¼0.04598) and
form (PC1: d¼0.05778; PC2: d¼0.02919) do not
differ significantly from the normal distribution. The
homogeneity of variance–covariance matrices was
checked using Bartlett’s test (D’Agostino & Russell,
1998). The results indicate that homogeneity of
variance–covariance matrices for shape (X2¼4.3852,
p¼0.2228) and form (X2¼3.8485, p¼0.2783) vari-
ables cannot be rejected.
In k-means clustering analysis, a set of specimens is
divided into k-groups fixed a priori in such a way that
the specimens within the k-groups are more similar to
one another than to specimens in the other clusters,
therebyminimisingwithin-groupvariation(MacQueen,
1967). The first step in this analysis is to define k
centroids, one for each cluster. The next step is to take
each specimen and associate it to the nearest centroid.
Then, k new centroids are re-calculated and the
specimens are associated to the nearest new centroid.
Consequently, a loop is generated, where k centroids
will change their location step by step until no more
changes are done. The k-means clustering is different
from discriminant analysis because no information
about the specimens is required, so the clusters are
generated based solely on the morphological similarity
among specimens. In this study, we classify the
individuals in two groups representing both sexes.
Then, we can assess grouping accuracy for individuals
in comparison with their actual sex.
Finally, four indices of sexual size dimorphism using
centroid size were examined: the mean distance index
Copyright # 2009 John Wiley & Sons, Ltd.
Int. J. Osteoarchaeol. (2009)
DOI: 10.1002/oa
P. N. Gonzalez, V. Bernal and S. I. Perez

Page 5

MDI ¼ Xm? Xf=Xm100
Xm=Xf
measurements were selected since their simplicity of
application permits comparisons with cases from the
literature and because of their widespread use in
physical anthropology (Marini et al. 1999).
Geometric morphometric analyses were performed
using tpsRelw 1.44 (Rohlf, 2007) and Semiland6
software (Sheets, 2003). All statistical analyses were
performed using R 1.9.1 (R Development Core Team,
2008).
??;theratiomale/female
??; the Student’s t-test and the F-test. These
Results
The values obtained by ICC show excellent agreement
(ICC>0.99; p<0.01) (Fleiss, 1981) between the two
series registered by the same observer (P.N.G.).
Likewise, high and significant values of ICC were
found between the three observers, both for RW1 and
RW2 (ICC>0.96 and p<0.01 for all comparisons).
Figure 2a is a plot of the first two relative warps
calculated from the landmarks and semilandmarks of
the craniofacial traits which account for 43.2% of the
explainedvariance.Malemorphologies—whichlocate
at the most negative values of first relative warp—
display a wider frontal and zygomatic processes as well
as a more developed glabella and mastoid process,
when compared to morphologies located at more
positive values (Figures 2b and c). In the shape space
represented by the first two relative warps, there is a
great superposition of males and females. Conversely,
in the shape–size space, both sexes are more
differentiated along the first principal component
(Figure3).Thefirsttwocomponents explain42.29%of
the total variance.
Figures 4a and b are box-plots of the discriminant
scores obtained using shape and form. These figures
show a great superposition between sexes when shape
variables are used, while they tend to separate when
size is incorporated to the analysis. The test of
significance also shows these differences. Although
both discriminant analyses were highly significant,
Wilks’ lambda for form was smaller (l¼0.650;
F¼34.530; p¼0.0000) than for shape variables
(l¼0.863; F¼10.217; p¼0.0001), indicating greater
differences between group means when shape and size
are analysed together.
The average accuracy obtained by discriminant
analysis based on shape variables was of 60.12%, and
slightly higher for females (64.15%) than for males
(60.75%) (Table 2). When multivariate statistical
analyses were performed using shape and size, the
percentages of correct estimations increased (Table 3).
The average accuracy obtained was 77.86%, with
similar percentages for females and males (76.9 and
78.48%, respectively).
The results obtained by k-means clustering based on
shape variables were 68.90% for average accuracy,
61.1% and 74.35% for females and males, respectively
(Table 2). The percentage of correct allocation by k-
means clustering of shape–size variables was 72.51%,
and was similar for both sexes (73.07% for females and
Figure 2. Relative warps of the craniofacial traits (a). The defor-
mation grids represent the variation along the first relative warp’s
axis, showing typically male (b) and female morphology (c). F:
female; M: male. The elipses represent 68% confidence intervals
for males and females.
Figure 3. Principal component analysis obtained with shape
and size variables. F: female; M: male. The elipses represent
68% confidence intervals for males and females.
Copyright # 2009 John Wiley & Sons, Ltd.
Int. J. Osteoarchaeol. (2009)
DOI: 10.1002/oa
Sexual Dimorphism of Cranial Traits